How to find the argument of a complex number?

Question

C++ / C#

I know that it is calculated through the angle φ, and depending on which quarter the number falls into, it will be decided how to find it: cos, sin, tg, arctg. But something is still difficult.

Answer 1

The argument of a complex number is always the arc tangent of the ratio of the imaginary part to the real part, taking into account a quarter.
In C, there is a special arc tangent atan2 for this.